Math 105 Test Two
Name:
1. (1 mark each)
a. f(x) = excos xfind f0(x) b. f(x) = bπln bfind Rf
c. f(x) = tan(2x+ 3) find f0(x) d. f(x) = ln xfind Rf
e. f(x) = cos x
1+sin2xfind Rf
1
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Math 105 Test Two: Derivatives and Limits, Exams of Calculus
Math 105 test two, which covers topics on derivatives and limits. The test includes questions on finding derivatives of various functions, evaluating limits, and using calculus to answer specific questions. Students are expected to use the limit definition of derivatives and basic calculus concepts to solve the problems.
Typology: Exams
2012/2013
1 / 7
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Math 105 Test Two
Name:
- (1 mark each) a. f (x) = ex^ cos x find f ′(x) b. f (x) = bπ^ ln b find
f
c. f (x) = tan(2x + 3) find f ′(x) d. f (x) = ln x find
f
e. f (x) = (^) 1+sincos^ x (^2) x find
f
- (5 marks) f (x) is a differentiable function and g(x) = f (ax) where a 6 = 0. Use the limit definition of derivative to show that g′(x) = af ′(ax).
- Use calculus to answer the following questions. a. (4 marks) Differentiate y = x + cos(xy) with respect to x.
b. (1 mark) A car drives on an elliptic track given by the graph of the equation 5 x^2 − 6 xy + 5y^2 = 16 where direction north is coincident with the positive y axis. At what points on the track is the car headed north or south?
b. (1 mark) A wire of length L is to be cut into two pieces. One piece will be used to form a square; the other, to form a circle. How should the wire be cut to maximize the sum of the areas of the pieces?